Solved 2 win 7 systems require login

[cma6]

I have a LAN with 4 systems: three Win 7 and one XP Pro. I have removed the Homegroup.
All the systems can see each other and access a shared folder with the exception of System1 and System (both Win 7), which require a user name/password to access the shared folder on the other system.
For example, if from System1 if I try to access System 2's shared folder, I get "Windows Security" login text entry window:
"Enter Network Password. Enter your password to connect to System2."
For "Username", I enter "\\system1".
For Password, I enter a password from the previous Home Group.
I can check "Remember credentias" but that works only until the next reboot.
Oddly, one sees under the "Password" text entry this: "Domain: System1" even though there is not domain, only a workgroup.
Likewise, from System2, I can access the shared folder on System1 by entering username "\\system2" with the same old homegroup password. Here I see "Domain: System2" even though there is no domain on System 2.
"Use usernames and passwords" is turned off in Advanced Sharing on all systems.
I want to get rid of this requirement to share between Systems 1 and 2.
Thanks in advance to the Windows experts.

 

[cma6]

I'm at the point now where of the 3 Win 7 Systems, #1, 2, and 3, the shares on System 3 can be seen by all the other systems and System 3 can see all the other shares. However, between System 1 and 2 there is a problem: although no no passoword is required (after reboot), for System 1 to see System 2, System 1 must log in with "\\System2" and vice versa. How can I get complete file sharing without logins?